Question

An object is placed at 4 cm distance in front of a concave mirror of radius of curvature 24 cm. Find the position of image. Is the image magnified?

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Answer

Radius of curvature (R) = 24 cm (negative)

Object distance (u) = 4 cm (negative)

Focal length (f) = 1\over 2 × 24 cm = 12 cm (negative)

Hence, focal length of the concave mirror = -12 cm.

1\over u + 1\over v = 1\over f

⇒ –1\over 4 + 1\over v = –1\over 12

1\over v = –1\over 12   + 1\over 4

1\over v = - 1+3\over 12

1\over v = 2\over 12

1\over v = 1\over 6

⇒ v = 6 cm

The image is formed 6 cm behind the mirror.

Computing linear magnification:

m = – 6\over -4 = 1.5

As, the length of image is 1.5 times the image of object, hence, the image is magnified.

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